# Small-scale Particle Clustering and Clustering Instability

__Description__

We predicted the effect of formation of small-scale inhomogeneities in
spatial distribution of inertial particles advected by turbulent flow. This effect can be of great
importance in various atmospheric and industrial flows, e.g., rain formation and fuel combustion in internal combustion engines.
We developed a comprehensive theory of clustering of inertial particles advected by a turbulent
velocity field caused by an instability of their spatial distribution.
The reason for the clustering instability is a combined effect of the particles inertia and a finite
correlation time of the velocity field. The crucial parameter for the clustering
instability is the size of the particles. The critical size of particles required
for excitation of the clustering instability is estimated for a strong clustering,
with a finite fraction of particles in clusters, associated with the growth of the mean absolute
value of the particle number density and for a weak clustering associated with the growth of the
second and higher moments. We introduced a new concept of compressibility of the turbulent diffusion
tensor caused by a finite correlation time of an incompressible velocity field. In this model of
the velocity field, the field of Lagrangian trajectories of particles is compressible. We suggested a
mechanism of saturation of the clustering instability associated with the particles collisions
in the clusters. An estimated nonlinear level of the saturation of the droplets number density in
atmospheric clouds exceeds by the orders of magnitude their mean number density. The critical size
of cloud droplets required for droplet cluster formation is of the order of 20 microns.

__References__

- T. Elperin, N. Kleeorin, and I. Rogachevskii, Self-Excitation of Fluctuations of
Inertial Particle Concentration in Turbulent Fluid Flow.
*Physical Review
Letters*, **77/27**, 5373-5376, 1996.

PDF: 191 KB

- T. Elperin, N. Kleeorin, I. Rogachevskii and D. Sokoloff, Turbulent Transport of
Atmospheric Aerosols and Formation of Large-Scale Structures.
*Physics and
Chemistry of Earth*, **25**, 797-803, 2000.

PDF: 825 KB

- Elperin T., Kleeorin N., L'vov V., Rogachevskii I. and Sokoloff D., The
Clustering Instability of Inertial Particles Spatial Distribution in Turbulent
Flows.
*Physical Review E*, **66**, 036302 (1-16), 2002.

PDF: 205 KB

- Elperin T., Kleeorin N., Liberman M., L'vov V., Rogachevskii I., Clustering of Aerosols in Atmospheric Turbulent Flow.
*Environ. Fluid Mech.*, **7**, 173-193, 2007.

PDF: 475 KB

- A. Khain, M. Pinsky, T. Elperin, N. Kleeorin, I. Rogachevskii, A. Kostinski, Critical comments to results of investigations of drop
collisions in turbulent clouds.
*Atmospheric Research*, **86**, 1-20, 2007.

PDF: 2.15 MB

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Department of Mechanical Engineering